x(2x+4)=12

Solution for x(2x+4)=12 equation:

Simplifying
x(2x + 4) = 12

Reorder the terms:
x(4 + 2x) = 12
(4 * x + 2x * x) = 12
(4x + 2x2) = 12

Solving
4x + 2x2 = 12

Solving for variable 'x'.

Reorder the terms:
-12 + 4x + 2x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + 4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 2x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + 2x + x2)' equal to zero and attempt to solve:

Simplifying
-6 + 2x + x2 = 0

Solving
-6 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 2x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + 2x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 2x + x2 = 0 + 6
2x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
2x + x2 = 6

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 6 + 1

Reorder the terms:
1 + 2x + x2 = 6 + 1

Combine like terms: 6 + 1 = 7
1 + 2x + x2 = 7

Factor a perfect square on the left side:
(x + 1)(x + 1) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(x + 1) equal to 2.645751311 and -2.645751311.

Subproblem 1
x + 1 = 2.645751311

Simplifying
x + 1 = 2.645751311

Reorder the terms:
1 + x = 2.645751311

Solving
1 + x = 2.645751311

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + x = 2.645751311 + -1

Combine like terms: 1 + -1 = 0
0 + x = 2.645751311 + -1
x = 2.645751311 + -1

Combine like terms: 2.645751311 + -1 = 1.645751311
x = 1.645751311

Simplifying
x = 1.645751311

Subproblem 2
x + 1 = -2.645751311

Simplifying
x + 1 = -2.645751311

Reorder the terms:
1 + x = -2.645751311

Solving
1 + x = -2.645751311

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + x = -2.645751311 + -1

Combine like terms: 1 + -1 = 0
0 + x = -2.645751311 + -1
x = -2.645751311 + -1

Combine like terms: -2.645751311 + -1 = -3.645751311
x = -3.645751311

Simplifying
x = -3.645751311

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.645751311, -3.645751311}
Solution
x = {1.645751311, -3.645751311}